Bubble Growth From First Principles

We consider the simplest relevant problem in the foaming of molten plastics, the growth of a single bubble in a sea of highly viscous Newtonian fluid, and without interference from other bubbles. This simplest problem has defied accurate solution from first principles. Despite plenty of research on foaming, classical approaches from first principles have neglected the temperature rise in the surrounding fluid, and we find that this oversimplification greatly accelerates bubble growth prediction. We use a transport phenomena approach to analyze the growth of a solitary bubble, expanding under its own pressure. We consider a bubble of ideal gas growing without the accelerating contribution from mass transfer into the bubble. We explore the roles of viscous forces, fluid inertia, and viscous dissipation. We find that bubble growth depends upon the nucleus radius and nucleus pressure. We begin with a detailed examination of the classical approaches (thermodynamics without viscous heating). Our failure to fit experimental data with these classical approaches, sets up the second part of our paper, a novel exploration of the essential decelerating role of viscous heating. We explore both isothermal and adiabatic bubble expansion, and also the decelerating role of surface tension. The adiabatic analysis accounts for the slight deceleration due to the cooling of the expanding gas, which depends on gas polyatomicity. We also explore the pressure profile, and the components of the extra stress tensor, in the fluid surrounding the growing bubble. These stresses can eventually be frozen into foamed plastics. We find that our new theory compares well with measured bubble behavior.

Bubble sizes in waters of the Atlantic Ocean

Typical size of bubbles obtained from cavitation inception pressure measured in the surface layer of the Atlantic Ocean in situ aboard R/V Professor Vize in 1971 and Nerey in 1973 are reported. These results do not contradict ones of bubble size measurements using optical or acoustical techniques. Variability of bubble size is discovered and described. This variability is related to passing from one geographical region to another (from 68°55'S to 61°52'N), to changes in depth (from 5 to 100 m) and in day time, as well as to spatial fluctuations within an aquatic area. It is suggested that, in addition to wave breaking, there is another source of bubbles at depth 10-20 m that associates with hydrobiological processes.

Extreme ultraviolet explorer : a view inside the bubble.

Cover title.

A study of data manipulation algorithms in magnetic bubble memories /

Thesis--Illinois.

A programming system for scanning digitized bubble-chamber negatives /

"This work was supported in part by the Atomic Energy Commission under contract No. AT(11-1)-1018."

Bubble scan I program /

"This work was supported in part by the Atomic Energy Commission under Contract No. AT(11-1)-1018"

MAC3D : numerical model for reservoir hydrodynamics with application to bubble diffusers /

"July 1998."

A High magnetic field bubble chamber : report of ORINS-ORNL Committee.

"ORINS-40; Particle accelerators and high-voltage machines."

The oil bubble.

Mode of access: Internet.

The bubble of the age; or, The fallacy of railway investment, railway accounts, and railway dividends.

Mode of access: Internet.

The Mississippi bubble; how the star of good fortune rose and set and rose again,

Mode of access: Internet.

The Garden of Earthly Delights Triptych, interior, center panel, lower portion, Birds and Couples, Couples in Bubble Flower

Hieronymus Bosch; grisaille, oil on wood

The Garden of Earthly Delights Triptych, interior, center panel, lower left: couple in bubble and conversing figures

Hieronymus Bosch; grisaille, oil on wood